If we had a pattern that went 0, 2, 4, 6, 8, 10. Instead of using one line, we can introduce 2 lines, such that we now have:
Instead of saying that the y-values (i.e. second row) is increasing by 2, we can say the y is twice what x is.
This is a lot more beneficial, because we know that if we assign , y is double, or
In the scenario that we didn’t know that y is twice x (i.e. , or alternatively, ), we would have had to extend the table much further to the right to find the correct answer, which is inefficient!
Note this time, that even though the increment is by 2, it is NOT any more. Rather, it is . As above, if we know , .
The above questions are therefore an example of “finding the formula”. Alternatively, there may be an instance where you have to insert in an x, to obtain a y.